How are you extracting the data from the source table? Is it possible that you are not actually extracting any data? If so, are loading all of the data that you are extracting . . . i.e. no data extracted means no data written.

Stick a dataviewer on the connection from datasource to see if anything emerges. Also, as Raph says, are you actually getting anything? - what's your datasource? - another table? If so, does your query depend on a data range that hasn't got anything in it, or hasn't been set up correctly?

I can see 16,000 rows when the job runs. Also if loading to a flat file data goes to the file, So there is sure data flowing.
I think the issue is I need to convert
DATE Filed from Datetime to Varchar 10
(2007-12-25 00:00:00.000) at Source

Which Data Type should I use under Data Conversion Transformation Editor, any ideas ?

"2007-12-25" is YYYY-MM-DD - a European format. What does your destination system want -- IOW show us what your destination system would store for Christmas Day 2007. Once you know the from and to formats you can work out how to get from one to the other.